Beauquier and Nivat introduced and gave a characterization of the class of pseudo-square polyominoes, i.e. those polyominoes that tile the plane by translation: a polyomino tiles the plane by translation if and only if its boundary word W may be factorized as W = XYX'Y'. In this paper we consider the subclass PSP of pseudo-square polyominoes which are also parallelogram. By using the Beauquier-Nivat characterization we provide by means of a rational language the enumeration of the subclass of psp-polyominoes with a xed planar basis according to the semi- perimeter. The case of pseudo-square convex polyominoes is also analyzed.

Brlek, S., Frosini, A., Rinaldi, S., & Vuillon, L. (2006). Tilings by translation: enumeration by a rational language approach. ELECTRONIC JOURNAL OF COMBINATORICS, 13(1), 1-24.

Tilings by translation: enumeration by a rational language approach

Rinaldi, S.;
2006

Abstract

Beauquier and Nivat introduced and gave a characterization of the class of pseudo-square polyominoes, i.e. those polyominoes that tile the plane by translation: a polyomino tiles the plane by translation if and only if its boundary word W may be factorized as W = XYX'Y'. In this paper we consider the subclass PSP of pseudo-square polyominoes which are also parallelogram. By using the Beauquier-Nivat characterization we provide by means of a rational language the enumeration of the subclass of psp-polyominoes with a xed planar basis according to the semi- perimeter. The case of pseudo-square convex polyominoes is also analyzed.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/10579
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